Method and apparatus for using entropy in ant colony optimization circuit design from high level synthesis

ABSTRACT

A method and apparatus for using entropy in ant colony optimization circuit design from high level synthesis is described. In one example, an operation to be performed by a circuit is selected. A plurality of hardware components for performing the operation are represented with a data flow graph having edges and nodes. A plurality of solutions for performing the operation are simulated as hardware component combinations represented as paths on the data flow graph. For each solution the cost including a number of edges and nodes traversed on the data flow graph and a supplemental sub-integer cost is determined and a solution is selected with the lowest cost as a hardware component combination for a circuit.

FIELD OF ART

The disclosed embodiments relate to circuit design, and moreparticularly to selecting solutions for time constrained scheduling ofoperations for a circuit design.

BACKGROUND

For the design of digital circuits (e.g., on the scale of Very LargeScale Integration (VLSI) technology), designers often employ computeraided techniques. Standard languages such as Hardware DescriptionLanguages (HDLs) have been developed to describe digital circuits to aidin the design and simulation of complex digital circuits. Severalhardware description languages, such as VHDL (Very high-speed integratedcircuit HDL) and Verilog HDL, have evolved as industry standards. VHDLand Verilog HDL are general purpose hardware description languages thatallow definition of a hardware model at the gate level, the registertransfer level (RTL), or the behavioral level using abstract data types.As device technology continues to advance, various product design toolshave been developed to adapt HDLs for use with newer devices and designstyles.

In designing an integrated circuit with an HDL code, the HDL source codedescribes the circuit elements, and a synthesis process produces an RTLnetlist from this source code. The RTL netlist is typically a technologyindependent netlist, in that it is independent of thetechnology/architecture of a specific vendor's integrated circuit, suchas a field programmable gate array (FPGA) or an application-specificintegrated circuit (ASIC). The RTL netlist corresponds to a schematicrepresentation of circuit elements (as opposed to a behavioralrepresentation). A mapping operation is then performed to convert fromthe technology independent RTL netlist to a technology specific netlistwhich can be used to create circuits in the vendor'stechnology/architecture. Field Programmable Gate Array (FPGA) vendorsuse different technologies and architectures to implement logic circuitswithin their integrated circuits. This results in a final netlist whichis specific to a particular vendor's technology and architecture.

High Level Synthesis (HLS) is a process of converting the behavioraldescriptions of HLD (High Level Description) to register transfer level(RTL) descriptions. HLS is typically done with a set of design goals andconstraints. So while there may be many different ways to implement thebehavior of the HLD, HLS seeks to do so while minimizing particulardefined costs. The defined costs are typically things such as cycletime, part count, silicon area, power, interconnections, pin count, etc.The constraints are typically driven by form factors, packagingconstraints, interoperability and similar concerns. HLS can be describedas compiling a specification written in a high level language (HLL),allocating hardware resources to the operations in the specification andthen generating the RTL description.

To generate the RTL description, the HLS schedules the operations,allocates the operation to particular functional hardware units,allocates any variables to storage elements, and allocates any datatransfers to communications buses that connect the functional units tostorage registers and input/output interfaces. In many devices,including Digital Signal Processors (DSP) the RTL description providesinputs and outputs of the system and the algorithms that are to beperformed. These are described as frames. Frame based algorithms aredescribed by using frame data. The input data is received in frames andthe output data is produced in frames.

Frame based algorithms are typically synthesized in HLS as follows:First the device collects the frame data from an input stream; then thedevice processes the frame data; and finally the device sends the outputframe as an output stream. The frame synthesis includes scheduling ofthe operations and binding the operations to hardware to obtain anoptimized device design. This methodology suffers from low throughput.

Ant Colony Optimization (ACO) is a recent optimization method that hasbeen applied to many different problems. In ACO, each ant constructs acandidate solution and leaves pheromones according to the costassociated with each solution it constructs. ACO allows severaldifferent solutions to be found. These can then be compared to eachother to find an optimum solution. ACO, however, has distinctlimitations that prevent it from being directly applied to existingsolution methodologies.

SUMMARY OF THE DESCRIPTION

A method and apparatus for using entropy in ant colony optimizationcircuit design from high level synthesis is described. In one example,an operation to be performed by a circuit is selected. A plurality ofhardware components for performing the operation are represented with adata flow graph having edges and nodes. A plurality of solutions forperforming the operation are simulated as hardware componentcombinations represented as paths on the data flow graph. For eachsolution the cost including a number of edges and nodes traversed on thedata flow graph and a supplemental sub-integer cost is determined. Asolution is selected with the lowest cost as a hardware componentcombination for a circuit.

BRIEF DESCRIPTION OF THE DRAWINGS

The disclosed embodiments are illustrated by way of example and notlimitation in the figures of the accompanying drawings in which likereferences indicate similar elements.

FIG. 1 is an example of a process flow diagram for performing high levelsynthesis for circuit design based on a high level description.

FIG. 2 is an example representation of a data flow graph for circuitdesign.

FIG. 3 is an alternative example representation of the data flow graphof FIG. 2.

FIG. 4 is a process flow diagram for one embodiment for pipeliningoperations for a circuit design using input and output data frames.

FIG. 5 shows one embodiment of a system for implementing the process ofFIG. 5.

FIG. 6 is an example of a process flow diagram for solving circuitdesign using ant colony optimization.

FIG. 7 shows one embodiment of a system for implementing the process ofFIG. 6.

FIG. 8 is an example of a process flow diagram for determining asupplementary cost of a circuit design for use in the process of FIG. 6.

FIG. 9 is an example of a process flow diagram of estimating aninterconnection cost for use in the process of FIG. 6.

FIG. 10 is an example of a process flow diagram of determining a guidingfunction for selecting solutions for use in the process of FIG. 6.

FIG. 11 is an example of a process flow diagram of determining afunction for selecting neighbors in a local search for use in theprocess of FIG. 6.

FIG. 12 is a block diagram example of a data processing systemconfigured for use with the disclosed embodiments.

DETAILED DESCRIPTION

At least one embodiment of the disclosed embodiments seeks to use an antcolony optimization (ACO) method to improve the design of an integratedcircuit. In one embodiment, an additional cost is added to the cost of acandidate solution to improve the selection of additional candidatesolutions.

High Level Synthesis (HLS) is a process that is used to convertbehavioral descriptions of a complex integrated circuit system to RTLdescriptions that can be used to construct the system. Some of thebehavioral descriptions may include frame synthesis, in which an inputframe and a corresponding output frame are described.

A basic process for designing a circuit with HLS is shown in the contextof FIG. 1. The process of FIG. 1 starts with establishing the high leveldescription, for example in HLD 102. This description will provide theoperations to be performed by the circuit, which may in one embodiment,include one or more types of partial operations. A partial operation isa portion of a larger operation that is performed to complete the largeroperation. For a multiplication operation, the partial operations mayinclude additions and register shifts. Embodiments can be applied to anytype of operations whether complete or partial. All operations whetherfull or partial, will be referred to herein simply as operations.

The operations in the HLD are identified at 104 and variables areassigned to the operations at 106. The variables for the operations areidentified and ordered based on the time order in which they will beused. The operations can be ordered based on this same time order at108. In one embodiment hardware components for performing theseoperations can be defined at 110.

There are different ways to determine the best combination of hardwarecomponents required to perform all of the operations. In one embodiment,different solutions for performing the operations are simulated ashardware component combinations at 114. Each solution is assigned a costat 112 and the solution with the lowest cost is selected at 116 as thehardware component combination for the final circuit design. Theselection and calculation of costs becomes an important part of findinga solution.

Frame-Based Input/Output

When the HLD to RTL system is applied to input and output data frames,the assignment of variables to hardware components becomes morecomplicated. If frames are processed individually, the resulting devicedescribed by the register transfer level description may be slower thannecessary. The efficiency and speed of the device can be increased byusing pipelined structures to process the frames. In a pipelinestructure, the processing elements are arranged so that the output ofeach element is the input to the next, and so that one operation isperformed per cycle.

A particular difficulty in frame synthesis for fully pipelinedarchitectures is mapping or binding the frame data to memory registers.The design of the memory mapping drastically affects the cost of themultiplexing logic and the control logic that is required to support thepipelined architecture. If the memory mapping is performed first, thenthere must be assumptions about the sequence of operations. Theseassumptions may turn out to be wrong after the scheduling algorithm iscompleted. On the other hand, if the scheduling is done first, then thescheduling algorithm may produce a solution which makes it difficult tomap the variables to at least some of the memory blocks. Therefore, inone embodiment, the scheduling algorithm to support pipelining is linkedto the corresponding binding algorithms and the memory mapping isperformed as part of the scheduling.

By integrating the frame synthesis with scheduling and bindingalgorithms, the Input/Output frame synthesis can be accommodated at thescheduling phase. In addition, input frame data that comes in apredetermined order, and input frame data that has no determined ordercan both be accommodated.

Scheduling and binding algorithms can be defined using a graph structureor data flow graph. Such a graph structure can be represented as (V, E,W). V is the set of operations v. Each operation has an operation type,which provides the hardware unit types upon which the correspondingoperation can be executed. As noted above, the term operation includespartial operations. E is the set of edges e which are the connectionsfrom one operation to another. W is a function which gives the registernumber w of an edge.

Data flow graphs can be composed of nodes that represent thecombinational computation units and edges interconnecting the nodes.Delays (e.g. registers) are represented as weights (w) on the edges.Each node has an execution time associated with it. Examples of dataflow graphs are shown in FIGS. 2 and 3 which illustrate a method toconstruct a data flow graph for retiming. FIGS. 2 and 3 are twodifferent representations of the same graph so that, for example, adder205 and 225 are the same adder. The combinational computation units(e.g., adder 205, multipliers 207 and 209) in FIG. 2 are represented ascomputation nodes (e.g., nodes 225, 227 and 229 in FIG. 3). FIG. 2 hasan input 201 and an output 203. The same path applies to FIG. 3.

The execution time of the combinational computation units can berepresented by the computation time of the associated nodes. Forexample, node 225 may have a computation time of 2 ns, which is requiredby adder 205; and each of nodes 227 and 229 may have a computation timeof 4 ns (nanoseconds), which is required by a multiplier (e.g., 209 or207). Edges represent connections between the computation units. Edge231 represents the connection between multiplier 207 and adder 205. Edge231 has a weight of 1, representing register 217 (or the one clock cyclelatency due to register 217). Similarly, edge 233 has a one clock cyclelatency due to register 215. Edge 235 represents the connection betweenmultipliers 209 and 207; and, there is no delay associated with edge235.

The data flow graph can be used to compare paths and latencies. Forexample, in FIG. 3, the path from node 229 to node 227 contains edge 235that has zero delay, but the path from node 229 to node 227 takes thelongest computation time (e.g., 8 ns, of which 4 ns are for node 229 and4 ns for node 227). Thus, the minimum clock period for the circuit inFIG. 2 is 8 ns. In FIG. 3, the delay on edge 233 can be moved to edge235 so that the critical path becomes the path between nodes 225 and229, which takes only 6 ns of computation time. Thus, moving the delayfrom edge 233 to edge 235, which can be implemented by moving register215 from between adder 205 and multiplier 209 to between multipliers 209and 207, allows the modified (retimed) circuit to be operated at areduced delay of 6 ns.

A timing model for a circuit module can be constructed by breaking downthe module into registers and combinational computing elements andassigning one node to each combinational computing element. The timingmodel of each hardware module is a combination of the timing models ofthe combinational computation units, delays, and interconnections. Theaggregation of the set of nodes and edges used in the translation of aparticular hardware module is effectively the timing model (data flowgraph) of that hardware module.

While a data flow graph can be represented by diagrams of the type shownin FIGS. 2 and 3, a data flow graph can also be represented in otherways, including by tables, text with metadata, and mathematicalequations. In the examples above, V, the set of values for v, arerepresented by the nodes, E, the set of values for e, are represented bythe edges between nodes, and W, the set of values for w, are representedby the registers on some of the edges.

Input and output frame data represents the input and the output data fora circuit that uses framed data. The data frames can be one dimensionalor multi-dimensional. Embodiments are described in the context of a onedimensional frame. However, the same principles can be used to extendthe principles to more dimensions. A one dimensional frame (F) can berepresented as a set of variables {v₁, v₂, v_(n)}, where n is the sizeof frame (|F|).

A pseudo code of a transformation algorithm to generate RTLspecifications for a given data flow graph (V, E, W) can be representedas follows:

for each input frame F do   define a unique operation type, t   for eachvariable v ε F   do    create a new operation op    set operation typeof op as t    add op to V    for each opConsume ε V    do       ifopConsume uses the v       do         create an edge e from op toopConsume         add e to the set E         set W(e) to zero       end   end   end end for each output frame F do   define a unique operationtype, t   for each variable v ε F   do    create a new operation op   set operation type of op as t    add op to the V    for each opSourceε V    do       if opSource produces the v       do       create an edgee from opSource to op       add e to the set E       set W(e) to zero   end   end end

In the above process op is a variable name that refers to a newlycreated operation for a variable of the frame. OpConsume refers to anoperation which takes a variable from the input frame as its input.OpSource refers to an operation which produces a variable of an outputframe as its output.

The above transformation may be performed for each variable of a frame.This provides a set of edges E that can be used to synthesize the frameinput/output (I/O). With the help of transformations such as thoseabove, frame synthesis problems can be solved while meeting schedulingand binding objectives. First, since each frame has its own uniqueoperation type, only one hardware unit can be assigned to a whole frameof data. This automatically converts the frame data to fully pipelinedserial data. The memory and multiplexing cost of the synthesized framecan also be minimized.

The transformation described above can be used for any serial inputsequence. If the serial sequence is predetermined, then the order of thesequence can be transformed to the schedules. In other words, theoperations which are produced by frame transformation are scheduled as apre-step of the scheduling algorithm. The pseudo code of this pre-stepcan be represented as follows:

for each op ε V do   if op is produced to represent variable v of frameF   do     set schedule of op to the order of the v in the sequence of F  end end

FIG. 4 shows a process flow diagram corresponding to one embodiment ofthe pseudocode example shown above. In FIG. 4 at 401, the variables fromthe input data frame of the high level description (HLD) are initializedfor all of the variables v of the data frame. At 402, operation typesare defined for each of the variables in the HLD. At 403, a newoperation (op) is created for one of the variables. As mentioned above,op is a variable name that refers to a newly created operation for thevariable of the frame. At 404, the new op is added to the operations ofthe data flow graph.

At 405, it is determined whether the variable is used by a ConsumeOp. AConsumeOp refers to an operation which takes a variable from the inputframe as its input. If a variable is not used by a consume operation,then an edge is created in the data flow graph from the new operationcreated at 403 to a consume operation. The process flow then continuesto 407 to determine whether there are any additional variables.

If the variable is used by a consume operation then it is determined at406 whether the variable is produced by a SourceOp. A source operationis an operation that produces a variable of the output frame. If thevariable is not produced by a source operation, then at 412, an edge iscreated in the data flow graph from a source operation to the newoperation created for that variable at 403. In addition, the weight onthat edge can be set at 0. After creating the edge, then the processcontinues to 407 to determine if there are any additional variables.

If the variable is produced by the source operation then at 407, it isdetermined whether there are any additional variables. If there areadditional variables, then the process flow returns to 402 to define anoperation type for the next variable. In one embodiment, this process isrepeated for all of the variables of an input data frame until all ofthe defined variables have been bound to consume operations and bound tosource operations.

After all the variables have been defined and connected to operationsthe process continues to 408, the variables can be ordered into a frame.In one embodiment this is done using conventional methodologies.

At 409, the operations can be ordered based on the order of thevariables. At 410 this process can be repeated for all of the additionalinput time frames. After all the input time frames have beencharacterized and defined in the data flow graph and bound tooperations, and after the operations have been ordered, in oneembodiment this information can be used to determine hardware componentcombinations as suggested in FIG. 2 at 210.

FIG. 5 shows one embodiment of frame binder modules for implementing theframe binding process. The system can be implemented as discretecomponents of an application specific integrated circuit (ASIC), digitalsignal processor (DSP), or another electronic device. The system may beimplemented in a software simulation system running on a computersystem. The modules of FIG. 5 include a high level description (HLD)analyzer 501 which is provides its analysis to an operation and variablebinder 503. The high level description analyzer 501 initializes all thevariables for a data frame, defines operation types, and createsoperations for each variable.

The HLD analyzer 501 is supplied by a high level description (HLD) 511.In one embodiment, the HLD 511 can be stored in any type of memory whichis available to the HLD analyzer 501 and provides to the operation andvariable binder 503, the operations, the variables, and the data framesthat are desired for the intended final circuit design. The operationand variable binder 503 binds variables to operations and bindsoperations to hardware types. In one embodiment, the operation andvariable binder 503 is coupled to a stored set of design constraints 513which establish the desired performance and hardware limitations and anyother design considerations intended to apply to the solutions.

The operation and variable binder 503 provides the bound operations andvariables to a solutions simulator 505. This simulator 505 createssolutions in the form of hardware modules and hardware connections. Thesolution in one embodiment can be created by reference to a data flowgraph or in a variety of other ways. The solutions from the solutionssimulator 505 are in one embodiment supplied to a cost estimator 507 andto a selection module 509. The selection module 509 in one embodimentlooks at each of the solutions and the costs of those solutions from theestimator 507 and selects a final design for the integrated circuitdesign.

As described above, an operation can be selected to be performed by theintegrated circuit that is to be designed. This operation can includeone or more partial operations of different types. In one example, theoperation may be a complex larger operation such as a mathematicalalgorithm, a conversion, or a transformation, and this operation mayinclude a variety of individual steps within that operation. Theseindividual steps can be treated as separate operations or as partialoperations within the overall operation.

The operations and the performance of the circuit can all be describedin the high level description. These operations are identified in theHLD, including any partial operations that may be a part of the overalloperations. The variables to be used by the operations are identifiedand ordered based on the times at which the variables will be used bythe partial or full operations. The partial operations can be orderedbased on the ordering of the variables. Solutions are developed using,for example, a solution simulator which represents different hardwarecomponents for performing the operations in any of a variety ofdifferent ways. In one embodiment, a data flow graph such as that shownin FIGS. 2 and 3 that has edges and nodes as explained above can be usedto simulate solutions.

The edges and nodes are connected based on the ordering of the partialoperations. Different solutions can be simulated for performing theseoperations, in one embodiment. The simulations represent the operationsas hardware component combinations and these combinations can berepresented as paths on the data flow graphs. For each of thesesolutions, a cost can be determined so that the different solutions canbe compared. The term “cost” can refer to a time to complete the path.The cost can be calculated in a wide range of different ways. A simpleapproach is to include the number of edges and nodes that are traversedto perform the entire solution on the data flow graph. The solution withthe lowest cost can be selected as the hardware component combinationfor the intended circuit design. In one embodiment, this process can berepeated until all of the operations of the high level description havebeen characterized and solutions have been found. In another embodiment,a subset of possible solutions may be evaluated.

The ordering of the operations can have a significant impact on thesolution. In one embodiment, the operations which produce a variable areordered after the operations that consume the variable are ordered. Inthe context of the description above, the consume operations are alldefined and ordered first then the source operations are ordered basedon the ordering of the consume operations. This helps to ensure thatwhenever a variable is consumed, the variable has been produced by aprior operation so that the variable is available for consumption.

Virtual Cost in ACO Pheromones

The quality of the resulting circuit depends on the quality of thesimulated solutions. With particularly complex circuits, the number ofpossible solutions becomes very large. Rather than simulate all possiblesolutions, techniques have been developed to try to simulate only thebest solutions. In some techniques, a baseline is established and theprocess tries to find solutions that are better than the baseline.Another technique for generating candidate solutions is referred to asAnt Colony Optimization (ACO) which attempts to optimize a solutionusing a technique modeled on how ants optimize a path between theircolony and a food source.

FIG. 6 shows a simplified process flow diagram for one embodiment ofACO. In FIG. 6, the parameters of the process are first initialized at601. In the case of transforming an HLD with high level synthesis (HLS)this initialization can include generating the operations and variables,and creating a net diagram including nodes and edges. One embodiment ofthe operations included in initialization is described above in thecontext of FIGS. 4 and 5.

Next a colony of virtual ants is created and a solution to the problemis constructed for each ant at 602. While colonies of several hundredants have been used, depending on the application ten or fewer willoften provide a good result. For each solution a local search isperformed at 603. The local search can select additional solutions orpaths. For each solution, the corresponding pheromones on the edges usedare updated at 605. The process repeats for all of the ants constructedat 602. When enough solutions have been generated at 604, the processends with a selection of one or more of the solutions based on thestrength of the pheromone trail of that solution.

The termination condition at 604 can be based on many different factors.Typically a predefined number of cycles is used. However, thetermination condition could be based on the variance in the cost of thesolutions, the amount of change in the pheromones, or more complexdeterminations, such as inflection points and graphed costs for theconstructed solutions.

In the example of FIG. 6, the selection of a solution is not shown as aseparate block because this is included in the local search at 603. Thelocal search 603 can compare a constructed solution at 602 to previoussolutions or to different local possibilities in order to select one ormore local solutions for simulation. In doing so, the prior solutionscan be compared to the current solution and a current best solution canbe determined. The pheromones can be updated based on the differencebetween the current solutions and the best prior solution. With such amethodology, a best solution is tracked. When the termination conditionis met, this best solution can be used as the final result.Alternatively, a separate process (not shown) can be used to examine allof the results and pick a best solution.

In some examples, solutions are produced one at a time. In oneembodiment for the example of FIG. 6, at 602, a single solution isconstructed and then one or a few neighboring solutions are constructedat 603. After the pheromones associated with the first solution aredeposited, then at 605, the pheromones for another solution and itsneighbors are deposited. In another embodiment 20 or 30 solutions areconstructed at each instance, compared, and then the local search triesto find a better neighboring solution for the best current solution.

While in real ant colonies, each ant leaves pheromones so that laterants can determine which paths have been more popular, in ACO, a costfactor is used as a pheromone to indicate which solutions are preferred.As a result, ACO can solve much more complex path problems with fewervirtual ants than would be required with a real ant colony. In theexample of FIG. 6, the pheromones are indicated as a delta factor at 605which is explained below for particular embodiments of the invention.

The process flow of FIG. 6 can be performed by hardware or softwaremodules as shown in FIG. 7 in one embodiment. As with FIG. 5, thesemodules can be implemented in hardware as discrete or blended functionalblocks of ASIC, DSP, or other circuitry. In another embodiment, thesemodules can be implemented in software on a computer system. As shown inFIG. 7, an ant construction module 703 generates one or more solutionsbased on the provided problem constraints. In one embodiment, thesolutions are then applied to a local search module 705. This modulesearches for neighboring solutions that may produce locally betterresults. In one embodiment, the best local solution selected by thelocal search module 705 can be fed back to the ant construction moduleso that a complete solution can be constructed and simulated. In oneembodiment, after each solution is simulated in the ant constructionmodule, pheromones are updated and stored in a memory 707. In anotherembodiment, each new solution is compared to the current best solution,and pheromones are updated based on that comparison. The pheromones canthen be used by the ant construction module to build and simulatesolutions and by the local search module to help guide the local search.In one embodiment, the entire system described in FIG. 7 corresponds tothe solution simulator 505 of FIG. 5.

One application of ACO is for time constrained scheduling (TCS) in thefield of integrated circuit design. However, it may be possible to applyACO to many other aspects of integrated circuit design. TCS tries toreduce the number of resources which are shared among a set ofoperations within a fixed number of time steps. In the context oftraditional TCS, the cost function associated with a schedule is themaximum number of operations scheduled to the same time step.

When applying ACO to TCS, ants tend to collect at local optima. In otherwords, the process will stagnate when a solution is reached that isbetter than the neighboring solutions, even when a better solution isavailable some distance away. The stagnation occurs because of plains(neighborhoods having the same cost function) in the solution space.This has been addressed by trying to better randomize the ants at thesolution construction phase. While this can cause the ants to stagnateat several different local optima, it does not cause the ants to trysolutions on a different solution plane after they have arrived at alocal optimum.

The ants select a solution based on the costs in the local search andthe costs in the pheromones. Adjusting these costs can change thebehavior of the ants. However, these costs are also used to select thebest solution, so any adjustment to the costs should consider its impacton the final design solution choice. In one embodiment, a virtual costfactor is added to the actual cost. The virtual cost factor is designedto change the shape of the solution space. The supplemental virtual costcan be used instead of the improved randomization techniques or as anaddition to it, depending on the application. The virtual cost can beused to guide the ants, but not to select a solution. Separating thisvirtual cost from actual costs can guide the ants within a plain ofsolutions without affecting the final design choice.

The plains within the solution space are caused by the cost function andare determined by how the cost function is traditionally (and naturally)defined. With a traditional definition, a large set of different butneighboring solutions are expected to have the same maximum number ofoperations scheduled to the same time step. Since the cost function isexpressed as a number of operations, it is an integer and this providesa “terraced landscape” in the solution space. In other words, manyneighboring solutions may have the same number of operations in a step,and many other neighboring solutions differ by one in either direction.The cost function does not provide a way to distinguish betweendifferent solutions that have the same maximum value for the number ofoperations.

This “terraced landscape” can be contoured in one embodiment with asub-integer supplemental cost factor. The sub-integer cost factor cangive values between the integer steps in order to give a “naturalcontinuous slope” to the solution space landscape. This allows the antsto use the sub-integer costs for local navigation and be guided towardslower local levels of cost.

A variety of different supplemental cost factors can be used. In oneembodiment, the supplemental cost factor is incorporated into the actualcost, supplementing the actual cost. This cost can then not be countedas cost for the solution. In another embodiment, the supplemental costfactor is virtual in the sense that it is not minimized for the finalsolution. It is used to enhance navigation. This can be done by using itto compare two candidate solutions whose traditionally defined integercosts are equal. The supplemental cost can then be used to favor asolution which is closer to a better solution.

A variety of different costs can be used as a supplemental costfunction, such as probabilities, variances, co-variances etc. In oneembodiment, a normalized entropy of the histogram of the operations onthe time steps (schedules) is used. With normalized entropy of thehistogram incorporated into the cost function, the cost for purposes ofthe pheromones can be calculated as the real cost (maximum number ofoperations per time step) minus the normalized entropy of the histogram.

In the context of time-constrained-scheduling by ant colonyoptimization, in one embodiment the ants' search at local optima can beinhibited from stagnating by incorporating this supplemental virtualcost factor into the traditional integer cost function.

A high level pseudo code of a basic ACO algorithm such as that of FIG. 6can be presented as follows:

Initialize parameters While termination condition is not met do  Construct solution for each ant   Apply local search   Updatepheromones End

There are different pheromone update strategies but in the area of TCS,it is common to use a solution (S) cost (C_(s)). In one embodiment, thisis applied to determine an incremental value (Δ_(ij)) of a pheromone ofan edge (_(ij)) between node i and node j in a data flow graph, such asthose of FIGS. 2 and 3. The better solution as indicated by thepheromone delta value will be the one that has the smaller delta or theleast amount of change. As mentioned above, while the pheromones arehelpful in guiding the selection of the next solution to simulate, thefinal solution is not selected based on pheromones but on actual cost.Due to the integer nature of the actual cost, there may be severalsolutions with the same lowest cost.

The incremental value Δ_(ij) can be determined as follows:

-   -   Δ_(ij)=1/Cs if ij belongs to S; otherwise 0    -   In a TCS algorithm the cost of the solution (C_(s)) can be        determined as follows:    -   Create an histogram array (HD) of the operation according to its        assigned time steps    -   Initialize HD to zero    -   For each operation, increment by one the value of HD [schedule        of operation]    -   C_(s) is the maximum value in HD

When a supplemental cost is used, the cost can be determined in oneembodiment the manner below:

-   -   Calculate the histogram (HD) as above    -   Define X as the time steps, an integer from 0 to tmax (where        tmax is the maximum number of time steps or time slots)    -   Probability P is from histogram; P=HD/N (where N is the number        of operations)    -   Normalized entropy;        H_(n)(X)=(1/log(Length(P)))*Sum{log(P(k))*P(k)}, where k=0 . . .        tmax    -   C_(s)=max{D}−H_(n)

The pseudocode above may be further illustrated by a concrete example.Consider an HLD which provides that there are 10 operations to beperformed and 4 time slots in which to perform them. The timeslots canbe labeled 0, 1, 2, 3. In this case N=10, tmax=4.

One solution might have the following schedule of operations (0, 2, 1,0, 3, 3, 1, 1, 1, 0) where each number corresponds to an operation, andthe numerical value corresponds to its timeslot. In this examplesolution, the operations may be scheduled so that:

-   -   3 operations are scheduled to time slot 0, so that HD(0)=3,    -   4 operations are scheduled to time slot 1, so that HD(1)=4,    -   1 operations is scheduled to time slot 2, so that HD(2)=1,    -   2 operations are scheduled to time slot 3, so that HD(3)=2    -   Therefore the histogram array HD=(3, 4, 1, 2).    -   The probability or length P=HD/N=HD/10=(0.3, 0.4, 0.1, 0.2).        This is the size of the sequence which is 4 which is equal to        tmax.    -   The entropy (E_(n)) then becomes the sum for each of the HD        values of (log(P(k)))(P(k) for k=1 to 4.    -   The P(k) sequence is (0.3, 0.4, 0.1, 0.2).    -   Allowing for some rounding, the entropy becomes:        (0.15+0.16+0.1+0.14)=0.55.    -   The normalized entropy (H_(n)) then becomes (1/log 4)*(0.55) or        1.6*0.55=0.88

Since there are no more than 4 operations in any one time step, max{HD}is 4 and the solution cost C_(s)=4-0.88=3.12. Modifying the integersolution cost by the non-integer entropy value allows similar solutionsto be differentiated. Of course, the number of decimals or level ofprecision can be increased to show even larger differences betweendifferent solutions. The level of precision can be adapted to suit anyparticular application. However, in one embodiment, the value of thesupplemental cost is small enough that it does not alter therelationship between solutions that already have different costsassociated with them. In one embodiment, the value of the supplementalcost is always less than one, since actual costs are calculated asintegers. While a particular approach to determining the entropy isprovided above, entropy may be determined in a variety of other ways.

FIG. 8 shows one embodiment of a process flow diagram for calculating avirtual cost. In FIG. 8 at 801 a histogram array of time steps iscreated. This histogram corresponds, in one embodiment, to the histogramarray identified as capital HD in the example above. At 803 the maximumvalue of HD is determined. At 805 the number of operations isdetermined. In one embodiment, this is assigned capital value N. At 807the probability of reinforcement (P) is calculated. The value of P isdetermined as HD/N.

At 809 these results are used to determine entropy as the sum of loggedfactors of each of the probabilities for each step. At 811 the entropycan be normalized based on the maximum value for HD, in one embodiment.The entropy may be normalized based on another value, in anotherembodiment.

At 813 the cost can be determined as a combination of an actual cost anda supplementary cost. In one embodiment, this cost can then be used inthe local search to further enhance the selection of solutions. In oneembodiment, as shown in the diagram of FIG. 7, the local search 705 canbe enhanced with a supplementary cost that is used in a solutionsimulator for designing an integrated circuit.

Given these applications, the design of an integrated circuit can beenhanced using a supplementary cost. In such a process, the operationsfrom a high level description or some other source are identified andthe hardware components for executing these operations are determined.This can be done with a data flow graph or in a variety of other ways.Given the operations and hardware components, a variety of differentsolutions are simulated for performing these operations.

The solutions are typically represented as hardware componentcombinations and interconnections, represented as paths on a data flowgraph for each solution. A cost is determined and this cost can includenot only the number of edge and nodes traversed on a data flow graph,but also the supplemental sub-integer cost such as entropy describedabove. The optimal solution can then be selected as the solution withthe actual lowest cost. In one embodiment, the supplemental cost is notincluded in this selection. In one embodiment, the supplemental cost issub-integer and therefore need not be excluded. The supplemental costcan be used in one embodiment for supplementing pheromone values in anant colony optimization technique.

Folding Transformations

Another technique that can be used in HLS is folding transformation.Rather than provide a unique hardware component for every partialoperation to be performed by a circuit, a circuit can be designed sothat the same hardware components can be used by different operations indifferent time steps. Paths are folded back to the same hardwarecomponent when the HLD is transformed through HLS. This allows the totalnumber of hardware components to be reduced. Folding transformationallows hardware units of a system to be shared among multiple operationsof the behavioral descriptions by time multiplexing. In other words,processes are folded back to a single hardware component, so that thecomponent serves different parts of different processes at differenttimes.

Folding depends upon the scheduling of operations and the binding ofoperations to particular hardware components. Scheduling can beconsidered to be a pre-process for folding and binding can be considereda primary sub-process of folding. For each operation, a schedulingalgorithm can determine a time step at which the operation is executedand a binding algorithm can determine a hardware unit upon which theoperation is executed.

With time-constrained scheduling, the number of operations executedduring any one time step can be minimized. This reduces the total numberof hardware units needed to support each time step. With feweroperations, folding becomes easier, further enhancing the potential costreductions. The binding algorithm can be used in one embodiment tominimize the number of interconnections between hardware components.This can reduce the cost of the hardware units and the overall circuitdesign. The interconnection cost in one embodiment includes routingregisters and the multiplexing logic to route data from one operation toanother.

For folding to reduce the cost or increase the efficiency of a circuit,it must be designed with scheduling and binding in mind. Scheduling istypically determined before binding. Folding requires moreinterconnections and folding determines, in part, the binding ofoperations to hardware components. As a result, all of these operationsare interrelated in one embodiment. The relationships can beaccommodated using iteration or using determinative processes. They canalso be accommodated with Ant Colony Optimization (ACO).

The results from ACO can be improved by adding some functions to thebasic ACO routine described, for example, in the context of FIG. 6. Inthe examples below, an interconnection cost function, a guidingfunction, and a local search neighbor selection function are described.These functions, in one embodiment, are combined to better considerinterconnections when adding folding to a circuit design. While allthree functions work well together, any one or more of the threefunctions can be used without the others depending on the particularapplication.

The interconnection cost function is related to the number of pairs ofcandidate folding edges and folding weights. The guiding function isrelated to a density function (ED) based on the probability of acandidate folding edge and folding weight pair in an unschedulednetlist. The neighbor selection function is related to the change ofthis density in edges connected to neighboring solutions. This densityfunction can be referred to as an edge density (ED) because it isdefined for edges. The density can be used to analyze and compare thenumbers of edges of different solutions. These functions are describedin more detail below.

The particular names of these functions are chosen to allow thefunctions to be identified and distinguished. The names and many aspectsof the functions can be modified to suit different applications. Thesefunctions allow the simulated solutions to take into account theinterconnection multiplexing cost during the scheduling, so that theoutput of scheduling is suitable to also minimize the interconnectioncost.

For any particular circuit design, the actual interconnection costoccurs as a result of the communication buses, registers, timing gates,multiplexers, and similar components that are required to interconnectthe hardware components of the circuit. Any circuit with an input and anoutput will have some cost for making connections. However, withfolding, the number of hardware components required can be decreased butthe interconnection cost can be significantly increased. The examplesbelow are described in the context of solutions with folding, but canalso be adapted to other types of circuit simulation.

Interconnection Cost and Folding Transformations

The interconnection cost is a real cost incurred in any circuit, asmentioned above. However, at the scheduling phase, the actualinterconnection cost cannot yet be determined. The actualinterconnection cost depends upon the binding results which are notknown until after scheduling is determined. An estimate can be made atthe scheduling phase and this can be used in an ACO context to guide theselection of candidate solutions and also to guide the final selectionof a solution. In this way, interconnection cost is considered even ifit is not precisely determined. In the context of FIG. 6, in oneembodiment the estimated interconnection cost can be used to selectlocal solutions at 603, and can also be used to enhance theeffectiveness of the pheromones at 605.

For the scheduling phase, the interconnection cost can be estimatedusing a candidate folded edge (cfe) and a folding weight (fw). Thenumber of different (cfe, fw) pairs can be taken as an estimate of thecost of the interconnection from multiplexing and other sources. The cfeis a candidate edge from a data flow graph in the final folded design. Afolded weight (fw) is the weight (w) of an edge (e) in the folded designand it is determined according to the folding formulation. This weightcan be used as a weight factor to scale the interconnection cost when itis added to the scheduling cost. In one embodiment, the weight isdetermined by the number of registers or delay states on the respectiveedge. This weight (w) corresponds to the weight w discussed above withrespect to creating the netlist.

Folding can be viewed as a function or a transformation which transformsa base design to a folded design. The aim of this transformation is toreduce the number of hardware components. This typically reduces thedesign area or the amount of space required for all of the components ofthe circuit. The circuit design as shown in FIGS. 2 and 3 can berepresented as a data flow graph or netlist structure with (V, E, w).

The netlist is a list of the logic gates of a circuit and theirinterconnections. It can be represented as a data flow graph. In thenetlist structure, V is the set of nodes v. A node in the base designbefore operations are bound to hardware refers to an operation. In thefinal folded design, the nodes refer to hardware units (HU). E is theset of edges e. An edge is a connection from one output port of anoperation to an input port of another operation as shown in FIGS. 2 and3. Each edge can be represented in the netlist by a quadruple withe=(sourceOperation, sourcePortAddress, targetOperation,targetPortAddress). Variable w is a function (w:=E->int) which gives thenumber of registers on an edge.

Scheduling in one embodiment determines the time step when eachoperation is executed. The time step assigned to an operation is calledthe schedule of the operation. Binding determines the hardware unit inwhich the scheduled operation is executed. If the scheduling isdetermined then the weight (fw) of the edge for the folded netlist canbe calculated for a particular edge e, which is a part of the set ofedges E (e εE), using a function referred to herein as FW.

In one example,

FW(e):=w(e)*foldingFactor+schedule(e.targetOperation)−schedule(e.sourceOperation)

-   -   where schedule (operation) refers to the time step at which an        operation is scheduled to be performed. This is typically        indicated by an integer count of the sequence of time steps.

To represent the interconnection cost at the scheduling phase, acandidate folded edge (cfe) can be defined. An edge definition for anedge of a final folded design netlist can be defined as being aconnection from one hardware unit to another hardware unit. This is whatis shown in e.g. FIG. 3. However, for the cfe, the hardware units arenot yet bound to any operations, so the cfe is defined by source anddestination hardware unit types instead. In other words, the cfe is apair (source hardware unit type, destination hardware unit type).

Another function, edge to candidate folding edge (e2cfe), can be defined(E->CFE) to determine corresponding cfe's for a given edge (e εE) of thebase design. In such a definition, E>CFE, that is the number of edges,e, exceeds the number of candidate folding edges, cfe.

The edge to candidate folding edge function (e2cfe) can be determined bycomparing hardware unite types to the underlying operations. Todetermine the e2cfe function, cfe.sourceHarwareUnitType=type ofe.sourceOperation, and cfe.destinationHardwareUnitType=type ofe.targetOperation. In other words, the e2cfe function is determinedbased on the operations between the source operation and the destinationoperation on either side of a candidate folding edge.

For a base netlist where the schedule of operations are determined, thenumber of different (cfe, fw) pairs can be used as an interconnectioncost function. In one embodiment, the number of different (cfe, fw)pairs can be used as an estimate of an actual interconnection cost.

Below is a pseudocode example of calculating interconnection cost. Inthis case, CFE_FW is a set of individual (cfe, fw) pairs.

The total interconnection cost can then be estimated as follows:

-   -   Total cost=C_(s)+interconnection cost, where T ε set of hardware        unit types.    -   Where C_(s) is the solution cost determined above in the context        of time constrained scheduling (TCS) using and colony        optimization (ACO)

Guiding Local Search in Folding Transformation

In one embodiment, the interconnection cost can be used in the solutionconstruction phase of the ACO. This is shown, in one embodiment, in FIG.6 as constructing a solution for each ant, 602. A guiding function canbe used in this phase to guide the construction of the solution. Avariety of different functions can be used. In one embodiment, describedbelow, a heuristic value is used to guide the ants when they areconstructing a solution. Another density function (ND) can be definedwhich gives the probability of the realization of a candidate foldingedge, folding weight (cfe, fw) pair in an unscheduled netlist. Thisdensity can be referred to as a node density. In this node entropycalculation uniformity is improved using the node density function, butin the interconnection cost case, all density is collected on somepoints which is the inverse of uniformity. In one example, the maximumof the node density value for an edge can be used as the heuristicvalue.

In the sub-process “construct solution” 602, in one embodiment, each antgenerates a schedule solution. During the generation of a solution,probabilities of choices are determined by the strength of thepheromones on a particular portion of the path. These probabilities canbe modified by the guiding function. This guiding function accommodatesthe interconnection cost by guiding the ants to a schedule whichgenerates the most frequently used (cfe, fw) pairs.

One embodiment of a node density function is defined in the pseudocodebelow. In this example, ASAP is a function which gives the minimumfeasible schedule value for a given operation. ASAP can be determined asthe earliest schedule for an operation which does not contradict withfeasibility constraints. For example, any values used in an operationmust be generated prior to the operation taking place. Similarly ALAP isa function which gives the maximum feasible schedule value for a givenoperation. ALAP can be determined as the latest schedule for anoperation which does not contradict with feasibility constraints. Forexample, if the results of an operation are used by a subsequentoperation, the operation must occur prior to that subsequent operation.These functions may be determined in any of a variety of ways well knownin the art.

Create table ND of size 2*|E|*FoldingFactor Reset all values of ND tozero. for each e ε E do   maxFW = w(e)*FoldingFactor −ASAP(e.sourceOperation) +   ALAP(e.targetOperation)   minFW = MAX(0,w(e)*FoldingFactor −   ALAP(e.sourceOperation) +ASAP(e.targetOperation))   for each fw in [minFW, maxFW]   do     index= h(e2cfe(e), fw)     ND[index] = ND[index] + 1 / (maxFW − minFW + 1)  end end

A guiding function which determines the heuristic value of setting theschedule of an operation to a particular selected schedule (sched) canbe determined in one embodiment as provided in the pseudocode below.

GUIDING-FUNCTION(o ε V , sched ε int, double table ND)   heuristicValue= 0   for each e ε E   do   if(e.sourceOperation is equal to o ore.targetOperation is equal to o)     if(e.sourceOperation is equal to o)    maxFW = w(e)*FoldingFactor − sched +     ALAP(e.targetOperation)    minFW = MAX(0, w(e)*FoldingFactor −     sched +ASAP(e.targetOperation))    else     maxFW = w(e)*FoldingFactor −    ASAP(e.sourceOperation) + sched     minFW = MAX(0,w(e)*FoldingFactor −     ALAP(e.sourceOperation) + sched)    for each fwin [minFW, maxFW]    do     index = h(e2cfe(e), fw)     heuristicValue =MAX(heuristicValue, ND[index])    end   end end return heuristicValue

The total heuristic value can be calculated as:

total heuristic value=(heuristic value for HU)*(heuristic value forinterconnection)

The heuristic value for each interconnection is calculated, in oneembodiment.

Neighbor Selection and Folding Transformation

In one embodiment, the local search 603 of FIG. 6 can be improved byconsidering the interconnection cost. A significant part of the localsearch is to select a particular neighbor to compare against.Calculating the cost for all of the possible neighboring solutions canbe complex and time-consuming. A neighbor selection function can producesimilar results more simply and in less time. In the embodimentdescribed below, the neighbor selection function uses the change indensity of the edges that connect an operation. The neighbor selectionfunction seeks to have more use of each interconnection. As a result,there may be fewer total interconnections in the final design. This isrepresented as a density value (ID).

In some versions of ACO, local search starts with a current or a bestsolution and searches for a better solution by evaluating neighboringsolutions and moving to the best neighboring solution. Neighbors can bedefined in different ways. One simple definition that will be used herefor illustrative purposes is that if the only difference betweensolution A and solution B is a schedule of one operation then A and Bare neighbors. In other words, solution A can be achieved by changingthe scheduling of only one operation in solution B.

In any real solution system, there will generally be several neighborsso the local search selects a particular one or more neighbors toevaluate. Rather than calculating the cost of all of the neighbors, themove which has the maximum value of the selection function can be chosenfor comparison. In one embodiment, this function is a density function(ID), defined from a (cfe, fw) pair to a double (CFE×int->double). Ifall the schedules are determined, the density function gives an integervalue which shows how many base design edges are mapped to a (cfe, fw)pair. Since in the context of local search all the schedules aredetermined, in one embodiment densities are integer values.

If all of the schedules are not determined, then in one embodiment theoutput of the density function (ID) is a higher precision floating pointnumber such as a double value, an integer, or a standard floating pointdecimal. This is described above in the context of defining the nodedensity function.

A hash function (h) can be used in one embodiment to generate a uniqueindex for each (cfe, fw) pair. The particular hash function can beselected based on the particular application and the level of precisiondesired. The output of h(cfe, fw) is an integer from 0 up to2*|E|*FoldingFactor. The FoldingFactor is a given value which definesthe maximum possible number of operations shared by a single hardwareunit. In one embodiment, I Density values (ID) for a schedule solutioncan be calculated as described in the following pseudocode example:

Create table ID of size 2*|E|*FoldingFactor Reset all values of ID tozero. for each e ε E do   index = h(e2cfe(e), FW(e))   ID[index] =ID[index] + 1 end

A selection function for changing an operation (o) schedule to a newschedule (newSched) can be represented in one embodiment as pseudocodeas follows:

SELECTION-FUNCTION(o ε V , newSched ε int, double table ID, maxDensity εint) selectionValue = 0 for each e ε E do   if(e.sourceOperation isequal to o or e.targetOperation is equal to o)   do     preDensity =ID(h(e2cfe(e), FW(e)))     if(e.sourceOperation is equal to o)      postFw = FW(e) + schedule(o) − newSched     else       postFw =FW(e) − schedule(o) + newSched     postDensity = ID(h(e2cfe(e), postFw))    if(postDensity + 1 > preDensity)       direction = +1     elseif(postDensity + 1 is equal to preDensity)       direction = 0     else      direction = −1   selectionValue = selectionValue + direction *(maxDensity −   MIN(preDensity, postDensity))   end end returnselectionValue

FIG. 9 is a process flow diagram of one embodiment of estimating aninterconnection cost. The process, in one embodiment, corresponds to thepseudocode representation described above. The interconnection cost canbe used, as mentioned above, for updating pheromones and for selectingneighbor solutions, for example in the process flow of FIG. 6.

At 901, candidate folding edges are determined for each edge in a dataflow graph for a potential solution. At 903, the source and targetoperations for each candidate folding edge (cfe) are determined. At 905,a folding weight (fw) is determined for each candidate folding edgeusing the source and target operations.

At 907, given the cfe and the fw, an interconnection cost can bedetermined for each edge of a solution based on the number of cfe, fwpairs associated with the edge. At 909, the interconnection cost can beweighted for each edge using the folding weight for that edge. At 911,the total interconnection cost is determined by adding up the values forall of the edges that are traversed for the solution. In one embodiment,these operations can be applied to the general integrated circuit designprocess of FIG. 2 in selecting hardware component combinations 210. Inthe ant colony optimization of FIG. 6 in one embodiment these operationscan be applied to updating pheromones as well as in the local search.

In one example, the use of an interconnection cost can begin with a highlevel description which includes one or more operations to be performedby the circuit that is being designed. A data flow graph or some otherrepresentation can be used to represent the hardware components thatwill be performing the operations. Different solutions are thensimulated for performing the operations in the HLD. These solutions canbe simulated as hardware component and schedule combinations. In thecase of a data flow graph, in one embodiment the combinations arerepresented as paths on the data flow graph.

Then for each solution, a cost is determined that includes, for example,the number of edges and nodes traversed on the data flow graph. Thiscost can be augmented with the interconnection cost, determined with theprocess flow diagram of FIG. 9 for example. The interconnection cost, asexplained above, is related to the number of different hardwarecomponents in the path. A pheromone trail can also be associated witheach path which includes a cost of the respective scheduling solution.The solution with the highest value pheromone trail can then be selectedas a hardware and schedule combination for the circuit. As indicated inFIG. 2, this can be repeated until all of the operations are scheduledand bound to hardware.

The candidate folding edges of FIG. 9 provide a way to represent thesteps for each solution. For a folding solution, each candidate foldingedge can have a source hardware type paired with a destination hardwaretype and be represented as an edge on the data flow graph. In oneembodiment, the interconnection cost can be weighted by the number ofdifferent types of hardware units used by the solution. In oneembodiment, this weight can represent the number of different types ofhardware units as a ratio of the number of hardware types for onesolution to the total number of different hardware types in the dataflow graph. The interconnection cost can also be weighted by the numberof registers used to perform the simulated solution. In one embodiment,the interconnection cost can further be weighted by a folding factorthat is related to the reuse of hardware resources. In one embodiment,the interconnection cost can further be weighted by a number of timesteps to perform the simulated solution.

A guiding function in one embodiment can be determined using the processflow diagram of FIG. 10. In FIG. 10 at 1001, the source and targetoperations are determined for each candidate folding edge. At 1003, thefolding weight is determined for each candidate folding edge. Theseoperations are similar to the operations 901 and 903 of FIG. 9 and inone embodiment the same values can be used reducing calculation stepsand the complexity of the overall solution. At 1005, an index can bedetermined for edges of the data flow graph using the number of (cfe,fw) pairs for each edge. An index is a unique value, in one embodimentdetermined using a hash function.

At 1007, the values for the current edge are compared to values forneighboring edges. At 1009, this comparison can be used to populate ahistogram array of time steps for the edges. At 1011, the maximum andminimum feasible schedule values are determined using the histogram.This maximum and minimum can represent the highest and lowest number oftime steps for the edges of each solution. At 1013, these determinedschedule values can be used to select the next solution to simulate. Thecomparison of the determined schedule values can be used, in oneembodiment, to guide the selection of the next solution in a localsearch, such as the one shown in FIG. 6. Such a local search in FIG. 2can in one embodiment guide the determination of which hardwarecomponent combination to simulate next, as shown in FIG. 2 at 210.

The guiding function of FIG. 10 can be applied to an overall circuitdesign process as in FIG. 2 by first selecting an operation to be formedby the circuit to be designed. The operation including any partialoperations can be represented with nodes on a data flow graph for eachof the hardware components performing the operations. Edges can be usedfor the paths between components. Solutions can then be simulated forperforming these operations as hardware component and schedulecombinations and represented as particular paths on the data flow graph.

Using the data flow graph, a cost can be determined for each solutionwhich includes for example a number of edges and nodes traversed on thepath and any other additional or supplemental costs. For an ant colonyoptimization routine, a pheromone trail can be associated with eachpath. Then, in one embodiment, as at 603 of FIG. 6, additional solutionsare simulated that neighbor the previous solutions. These solutions canbe selected using a neighbor selection function, such as the onediscussed with respect to FIG. 10 which is based on a number ofoperations performed by hardware components that neighbor the hardwareunits used by a solution. Eventually, a solution with the lowest cost ora low cost can be selected for the integrated circuit design.

The neighbor selection function can be designed to compare the number ofoperations performed using different schedules that start at differentedges on the data flow graph to perform the same operation. Thisfunction can be a function of the edge density, or the density offolding operations for each edge that neighbors the initial edge of arespective solution. The next solution to be selected in the localsearch can be a solution which maximizes the density function thatpresents the greatest positive change, or presents the greatestdifference in the density. Alternatively, the neighbor selectionfunction can determine an index for each edge of the graph based on thenumber of operations in a particular solution and the amount of foldingfor each included edge. Then the next solution to be selected can be onethat has the highest index of the candidates considered.

FIG. 11 shows a process flow diagram of one embodiment for determining aneighbor selection function. This function can be used in the localsearch 603 of an ant colony optimization for example. At 1101, ahistogram array of time steps is determined. At 1103, source and targetoperations are determined for each candidate folding edge. In oneembodiment, prior to this process flow, the folding is determined andcandidate folding edges are presented. In one embodiment, the processesdescribed above for FIGS. 9 and 10 may be used to do this.

At 1105, a folding weight is determined for each candidate folding edgeand, at 1107, indices are determined for the edges of the data flowgraph. These indices can be determined using the number of (cfe, fw)pairs for each edge. At 1109, the index for a current edge is comparedto indices for neighboring edges and at 1111, using this comparison, theneighboring edge with the highest index can be selected as the nextsolution to simulate. This process can be repeated to evaluateadditional solutions.

In the context of FIG. 11, an integrated circuit design can be augmentedwith a guiding function. As mentioned before, the operations to beperformed by the integrated circuit design are characterized, forexample, using high level description and the hardware components forperforming this operation can be represented on a data flow graph withedges between the hardware components. The guiding function can be usedto select from among different solutions for performing the operations.The solutions, similar to those described above with respect to FIGS. 9and 10, can be represented as hardware components and schedulecombinations represented on the graph. The costs for each simulation aredetermined and then a solution with the lowest cost is selected. Theguiding function can be related to the amount of hardware reuse on anedge of the data flow graph for the particular solution. This can becombined with pheromone trails to select a solution with a lower cost.

This description and drawings are illustrative of embodiments of theinvention and are not to be construed as limiting the invention.Numerous specific details are described to provide a thoroughunderstanding of the disclosed embodiments. However, in certaininstances, well known or conventional details are not described in orderto avoid obscuring the description of the disclosed embodiments.References to an or one embodiment in the present disclosure are notnecessarily to the same embodiment; and, such references mean at leastone.

In the present description and in the claims, a register refers to asequential element in general (e.g., a delay element, a memory cell, aflip-flop, or others). A register samples and holds (stores) the inputsignal so that it can be output in synchronization with the clock of thecircuit. Further, it is understood that one delay on an edge of a dataflow graph represents a unit of latency typically introduced by thepresence of a register on the corresponding path. However, the unit oflatency can also be introduced through other means, such as differentcontrol signals for reading a memory cell, multiplexers, dividers, orpath delays.

Many of the methods of the disclosed embodiments may be performed with adigital processing system, such as a conventional, general-purposecomputer system. Special purpose computers, which are designed orprogrammed to perform only one function, may also be used.

FIG. 12 shows one example of a typical computer system which may be usedwith the disclosed embodiments. For example, it is noted that theprocesses described with respect to FIGS. 1-4, 6, and 8-11 areoperational through the example computing system. In addition, themodules described in FIGS. 5 and 7 are configurable in a data processingsystem structured similar to the example computing system. However, itis noted that while FIG. 12 illustrates various components of a computersystem, it is not intended to represent any particular architecture ormanner of interconnecting the components but rather provides an examplerepresentation of how the components and architecture may be configured.It will also be appreciated that network computers and other dataprocessing systems which have fewer components or perhaps morecomponents may also be used with the disclosed embodiments. The computersystem of FIG. 12 may be any computing system capable of performing thedescribed operations.

As shown in FIG. 12, the computer system 1201, which is a form of a dataprocessing system, includes a bus 1202 which is coupled to amicroprocessor 1203. In one embodiment, computer system 1201 includesone or more of a read only memory (ROM) 1207, volatile memory (RAM)1205, and a non-volatile memory (EEPROM, Flash) 1206. The microprocessor1203 is coupled to cache memory 1204 as shown in the example of FIG. 12.Cache memory 1204 may be volatile or non-volatile memory.

The bus 1202 interconnects these various components together and in oneembodiment interconnects these components 1203, 1207, 1205, and 1206 toa display controller and display device 1208. The computer system 1201may further include peripheral devices such as input/output (I/O)devices which may be mice, keyboards, modems, network interfaces,printers, scanners, video cameras and other devices which are well knownin the art. Typically, the input/output devices 1210 are coupled to thesystem through input/output controllers 1209.

The volatile RAM 1205 is typically implemented as dynamic RAM (DRAM)which requires power continually in order to refresh or maintain data inthe memory. The non-volatile memory 1206 is typically a magnetic harddrive, magnetic optical drive, an optical drive, a DVD RAM, a Flashmemory, or other type of memory system which maintains data even afterpower is removed from the system. Typically, the non-volatile memorywill also be a random access memory although this is not required.

While FIG. 12 shows that the non-volatile memory is a local devicecoupled directly to the rest of the components in the data processingsystem, it will be appreciated that the disclosed embodiments mayutilize a non-volatile memory which is remote from the system, such as anetwork storage device which is coupled to the data processing systemthrough a network interface such as a modem or Ethernet interface.

The bus 1202 may include one or more buses connected to each otherthrough various bridges, controllers and/or adapters as is well known inthe art. In one embodiment the I/O controller 1209 includes a USB(Universal Serial Bus) adapter for controlling USB peripherals, and/oran IEEE-1394 bus adapter for controlling IEEE-1394 peripherals.

It will be apparent from this description that aspects of the disclosedembodiments may be embodied, at least in part, in software (orcomputer-readable instructions). That is, the techniques, for examplethe processes of FIGS. 1-4, 6, and 8-11, may be carried out in acomputer system or other data processing system in response to itsprocessor, such as a microprocessor, executing sequences of instructionscontained in a memory, such as ROM 1207, volatile RAM 1205, non-volatilememory 1206, cache 1204 or a remote storage device. In variousembodiments, hardwired circuitry may be used in combination withsoftware instructions to implement the disclosed embodiments. Thus, thetechniques are not limited to any specific combination of hardwarecircuitry and software nor to any particular source for the instructionsexecuted by the data processing system. In addition, throughout thisdescription, various functions and operations are described as beingperformed by or caused by software code to simplify description.However, those skilled in the art will recognize what is meant by suchexpressions is that the functions result from execution of the code by aprocessor, such as the microprocessor 1203.

A machine readable medium can be used to store software and data whichwhen executed by a data processing system causes the system to performvarious methods of the disclosed embodiments. This executable softwareand data may be stored in various places including for example ROM 1207,volatile RAM 1205, non-volatile memory 1206 and/or cache 1204 as shownin FIG. 12. Portions of this software and/or data may be stored in anyone of these storage devices.

Thus, a machine readable medium includes any mechanism that stores anyinformation in a form accessible by a machine (e.g., a computer, networkdevice, personal digital assistant, manufacturing tool, any device witha set of one or more processors, etc.). For example, a machine readablemedium includes recordable/non-recordable media (e.g., read only memory(ROM); random access memory (RAM); magnetic disk storage media; opticalstorage media; flash memory devices; etc.).

In the foregoing specification, the disclosed embodiments have beendescribed with reference to specific exemplary embodiments thereof. Itwill, however, be evident that various modifications and changes may bemade thereto without departing from the broader spirit and scope of theinvention as set forth in the appended claims. The specification anddrawings are, accordingly, to be regarded in an illustrative rather thana restrictive sense.

1. A method comprising: selecting an operation to be performed by acircuit; representing, through a data flow graph having edges and nodes,a plurality of hardware components for performing the operation;simulating a plurality of solutions for performing the operation, eachsolution corresponding to a hardware component combination representedas a path on the data flow graph; determining a cost for each solutionof the plurality of solutions, the cost including a number of edges andnodes traversed on the data flow graph and a supplemental sub-integercost; and selecting a solution from among the plurality of solutions,the selected solution having a lowest determined.
 2. The method of claim1, wherein the supplemental sub-integer cost is a virtual cost.
 3. Themethod of claim 1, wherein the supplemental cost is a normalized valueof an entropy of a number of steps to complete the respective solution.4. The method of claim 1, wherein the supplemental sub-integer cost isbased on a value of an entropy of a histogram of operations
 5. Themethod of claim 1, wherein determining a cost comprises creating ahistogram array of a number of steps of each simulated solution.
 6. Themethod of claim 5, wherein the number of steps comprises the number ofedges traversed on the data flow graph for each solution.
 7. The methodof claim 6, further comprising determining a probability of eachsimulated solution based on the histogram value and the number ofoperations of the respective solution and wherein the supplementalsub-integer cost is a function of the probability.
 8. The method ofclaim 1, wherein simulating a plurality of solutions comprisessimulating each step through the data flow graph for each solution, eachstep comprising traversing an edge between two nodes of the data flowgraph.
 9. The method of claim 8, further comprising associating apheromone trail with each traversed edge.
 10. The method of claim 1,wherein simulating a plurality of solutions comprises heuristicallysearching for local solutions.
 11. The method of claim 1, whereinsimulating a plurality of solutions comprises performing an ant colonyoptimization and wherein determining a cost further comprises applying acost to increment a pheromone value of an edge in the data flow graph.12. A non-transitory computer-readable medium storing instructionsthereon, the instructions when executed by a processor causing theprocessor to: select an operation to be performed by a circuit;represent, through a data flow graph having edges and nodes, a pluralityof hardware components for performing the operation; simulate aplurality of solutions for performing the operation, each solutioncorresponding to a hardware component combination represented as a pathon the data flow graph; determine a cost for each solution of theplurality of solutions, the cost including a number of edges and nodestraversed on the data flow graph and a supplemental sub-integer cost;and select a solution from among the plurality of solutions, theselected solution having a lowest determined cost.
 13. Thecomputer-readable medium of claim 12, wherein determining a costcomprises creating a histogram array of a number of steps of eachsimulated solution.
 14. The computer-readable medium of claim 13,wherein the number of steps comprises a number of edges traversed on thedata flow graph for each solution.
 15. The computer-readable medium ofclaim 14, further comprising determining a probability of each simulatedsolution based on a histogram value and a number of operations of therespective solution and wherein the supplemental sub-integer cost is afunction of the probability.
 16. The computer-readable medium of claim12, wherein simulating a plurality of solutions comprises simulatingeach step through the data flow graph for each solution, each stepcomprising traversing an edge between two nodes of the data flow graph.17. The computer-readable medium of claim 16, further comprisingassociating a pheromone trail with each traversed edge.
 18. A digitalprocessing system comprising: means for selecting an operation to beperformed by a circuit; means for representing, through a data flowgraph having edges and nodes, a plurality of hardware components forperforming the operation; means for simulating a plurality of solutionsfor performing the operation, each solution corresponding to a hardwarecomponent combination represented as a path on the data flow graph;means for determining a cost for each solution of the plurality ofsolutions, the cost including a number of edges and nodes traversed onthe data flow graph and a supplemental sub-integer cost; and means forselecting a solution from among the plurality of solutions, the selectedsolution having a lowest cost.
 19. The system of claim 18, wherein thesupplemental sub-integer cost is a normalized value of an entropy of anumber of steps to complete the respective solution.
 20. The system ofclaim 18, wherein the supplemental sub-integer cost is based on a valueof an entropy of a histogram of operations.
 21. An apparatus comprising:a memory to store a data flow graph representing a plurality of hardwarecomponents for performing at least one operation, the data flow graphhaving edges and nodes; a solution simulator coupled to the memory toreceive the data flow graph and to simulate a plurality of solutions forperforming the operation as hardware component combinations representedas paths on the data flow graph; a cost estimator coupled to thesolution simulator to receive the solutions and to determine a cost foreach solution, the cost including a number of edges and nodes traversedon the data flow graph and a supplemental sub-integer cost; and asolution selector coupled to the cost estimator to receive the estimatedcosts and to select a solution with the lowest cost as a hardwarecomponent combination for a circuit.
 22. The apparatus of claim 21,further comprising an operation and variable binder to bind variable tothe operation before supplying the data flow graph to the solutionsimulator.
 23. The method of claim 21, wherein the supplemental cost isbased on a value of the entropy of a histogram of operations